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Journal Article

Logarithmic de Rham comparison for open rigid spaces


Pan,  Xuanyu
Max Planck Institute for Mathematics, Max Planck Society;

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Li, S., & Pan, X. (2019). Logarithmic de Rham comparison for open rigid spaces. Forum of Mathematics, Sigma, 7: e32. doi:10.1017/fms.2019.27.

Cite as: https://hdl.handle.net/21.11116/0000-0004-F94A-1
In this note, we prove the logarithmic $p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally $K(\pi,1)$ (in a certain sense) with respect to $\mathbb{F}_p$-local systems and ramified coverings along the divisor. We follow Scholze's method to produce a pro-version of the Faltings site and use this site to prove a primitive comparison theorem in our
setting. After introducing period sheaves in our setting, we prove aforesaid comparison theorem.